Matrix Models, Integrable Structures, and T-duality of Type 0 String Theory

Abstract

Instanton matrix models (IMM) for two dimensional string theories are obtained from the matrix quantum mechanics (MQM) of the T-dual theory. In this paper we study the connection between the IMM and MQM, which amounts to understand T-duality from the viewpoint of matrix models. We show that type 0A and type 0B matrix models perturbed by purely closed string momentum modes (or purely winding modes) have the integrable structure of Toda hierarchies, extending the well known results for c=1 string. In particular, we show that type 0A(0B) MQM perturbed by momentum modes has the same integrable structure as type 0B(0A) MQM perturbed by winding modes, which is a nontrivial check of the T-duality between the matrix models. The MQM deformed by NS-NS winding modes are used to study type 0 string in 2D black holes. We also find an intriguing connection between the IMM and the MQM via tachyon condensation. The array of alternating D-instantons and anti-D-instantons separated at the critical distance plays a key role in this picture. We discuss its implications on sD-branes in two dimensional string theories.

41 pages, 2 figures

References in corpus (14)

• Strings from Tachyons
• Classical and Quantum D-branes in 2D String Theory
• Closed Strings as Imaginary D-branes
• Branes in the 2D black hole
• Matrix Cosmology
• Flux Backgrounds in 2D String Theory
• Two-dimensional superstrings and the supersymmetric matrix model
• A Matrix Model for AdS2
• On the S-matrix of Type 0 String Theory
• Type 0 Strings in a 2-d Black Hole
• Topological Matrix Models, Liouville Matrix Model and c=1 String Theory
• Non-Perturbative String Equations for Type 0A
• Renormalization Group Approach to $c=1$ Matrix Model on a circle and D-brane Decay
• Nonsinglet Sector of $c=1$ Matrix Model and 2D Black Hole

Cited by in corpus (18)

• Liouville Field Theory -- A decade after the revolution
• Flux Backgrounds in 2D String Theory
• Flux-vacua in Two Dimensional String Theory
• On Black Hole Thermodynamics of 2-D Type 0A
• Boundary Ground Ring in 2D String Theory
• Superstrings on AdS_2 and Superconformal Matrix Quantum Mechanics
• c=1 Matrix Model from String Field Theory
• c < 1 String from Two Dimensional Black Holes
• Scattering of Long Folded Strings and Mixed Correlators in the Two-Matrix Model
• Topological B-model and $\hat{c}=1$ String Theory
• Proposal for the Open String Tachyon Effective Action in the Linear Dilaton Background
• Long Strings and Chiral Non-Singlets in Matrix Quantum Mechanics
• Noncritical String Correlators, Finite-N Matrix Models and the Vortex Condensate
• Open/closed duality for FZZT branes in c=1
• Condensing Momentum Modes in 2-d 0A String Theory with Flux
• On the Spectrum of D=2 Supersymmetric Yang-Mills Quantum Mechanics
• Integrable Deformations of $\hat{c}=1$ Strings in Flux Backgrounds
• A Note on Tachyon Moduli and Closed Strings